Skip to main content
SpringerLink
Log in

The Einstein-Kähler metric on the third Cartan-Hartogs domain

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper we discuss the Einstein-Kähler metric on the third Cartan-Hartogs domain Y III (n, q;K). Firstly we get the complete Einstein-Kähler metric with explicit form on Y III (n, q;K) in the case of K = q/2 + 1/q−1. Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature. Finally we prove that the complete Einstein-Kähler metric is equivalent to the Bergman metric on Y III (n, q;K) in case of K = q/2 + 1/q−1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cheng, S. Y., Yau, S. T.: On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation. Comm Pure Appl Math., 33, 507–544 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  2. Mok, N., Yau, S. T.: Completeness of the Kähler-Einstein metric on bounded domain and the characterization of domain of holomorphy by curvature conditions. Proc Symposia Pure Math., 39, 41–59 (1983)

    MathSciNet  Google Scholar 

  3. Yin, W. P.: Cartan Domain to Hua Domain, Capital Normal University Press, Beijing, 413–430, 287–310, 2003

    Google Scholar 

  4. Wang, A., Yin, W. P., Zhang, W. J.: Einstein-Kähler metric on Cartan-Hartogs domain of the third type [J]. Advances In Mathematics, 33(2), 215–228 (2004)

    MathSciNet  Google Scholar 

  5. Wang, A., Yin, W. P.: Einstein-Kähler metric with explicit formula on Super-Cartan domain of the fourth type. Acta Mathematica Sinica, English Series, 22(2), 367–376 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Wang, A., Yin, W. P., Zhang, L. Y., Roos, G.: The Kähler-Einstein metric for some Hartogs domains over bounded symmetric domains. Science in China Ser. A Mathematics, 49(9), 1175–1210 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lu, Q. K.: The Classical Manifolds and the Classical Domains, Shanghai Scientific and Technical press, Shanghai, 1963

    Google Scholar 

  8. Yin, W. P.: Curvatures and invariant functions. Scientia Sinica Ser. A, 31(6), 675–686 (1988)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Wen Juan Zhang

  2. Department of Mathematics, Capital Normal University, Beijing, 100037, P. R. China

    Wei Ping Yin

Authors
  1. Wen Juan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Ping Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen Juan Zhang.

Additional information

The research is supported by the NSF of China (Grant NO. 10471097)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, W.J., Yin, W.P. The Einstein-Kähler metric on the third Cartan-Hartogs domain. Acta. Math. Sin.-English Ser. 24, 1703–1712 (2008). https://doi.org/10.1007/s10114-008-6548-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-008-6548-y

Keywords

MR(2000) Subject Classification

Search

Navigation